We construct examples of translationally invariant solvable models of strongly-correlated metals, composed of lattices of Sachdev-Ye-Kitaev dots with identical local interactions. These models display crossovers as a function of temperature into regimes with local quantum criticality and marginal-Fermi liquid behavior. In the marginal Fermi liquid regime, the dc resistivity increases linearly with temperature over a broad range of temperatures. By generalizing the form of interactions, we also construct examples of non-Fermi liquids with critical Fermi-surfaces. The self-energy has a singular frequency dependence, but lacks momentum dependence, reminiscent of a dynamical mean field theory-like behavior but in dimensions $dless than \infty$. In the low temperature and strong-coupling limit, a heavy Fermi liquid is formed. The critical Fermi-surface in the non-Fermi liquid regime gives rise to quantum oscillations in the magnetization as a function of an external magnetic field in the absence of quasiparticle excitations. We discuss the implications of these results for local quantum criticality and for fundamental bounds on relaxation rates. Drawing on the lessons from these models, we formulate conjectures on coarse grained descriptions of a class of intermediate scale non-fermi liquid behavior in generic correlated metals.

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具有临界费米表面的平移非费米液态金属：可求解模型

我们构建强相关金属的平移不变可溶模型的示例，该模型由具有相同局部相互作用的Sachdev-Ye-Kitaev点的晶格组成。这些模型显示了温度随温度的变化，进入具有局部量子临界和边际费米液体行为的状态。在边缘费米液体状态下，直流电阻率在很宽的温度范围内随温度线性增加。通过概括相互作用的形式，我们还构造了具有临界费米表面的非费米液体的例子。自能量具有奇异的频率依赖性，但缺乏动量依赖性，让人联想到类似动力学平均场论的行为，但维度小于\ infty $。在低温和强耦合极限下，形成重的费米液体。在没有费米液体激发的情况下，非费米液体状态下的临界费米表面会在磁化强度中引起量子振荡，这是外部磁场的函数。我们讨论了这些结果对局部量子临界性和弛豫率基本界限的影响。借鉴这些模型的经验教训，我们对一般相关金属中的一类中等规模非费米液体行为的粗粒度描述进行了猜想。